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GEOMETRY: Chapter 10 10.1: Tangents to Circles

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**A chord is a segment whose endpoints are on a circle. **

A circle is the set of all points in a plane that are equidistant from a given point called the center of the circle. A circle with center P can be written P. A segment whose endpoints are the center of any point on the circle is a radius. A chord is a segment whose endpoints are on a circle. A diameter is a chord that contains the center of a circle. Image taken from:http://www.pecoglassbending.com/images/Circle%20terms.jpg

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**A secant is a line that intersects a circle in two points**

A secant is a line that intersects a circle in two points. A tangent is a line in the plane of a circle that intersects the circle in exactly one point, the point of tangency. The tangent ray and the tangent segment are also called tangents. Image taken from:

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Ex.1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. Image taken from: Geometry. McDougal Littell: Boston, P. 652.

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Ex.1: Tell whether the line or segment is best described as a radius, chord, diameter, secant, or tangent of circle C. Answer: a) radius; b) secant; c) diameter; d) tangent Image taken from: Geometry. McDougal Littell: Boston, P. 652.

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**Ex.2: Use the diagram to find the given lengths.**

Radius of circle B Diameter of circle A Radius of circle A Diameter of circle B Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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**Ex.2: Use the diagram to find the given lengths.**

Radius of circle B Diameter of circle A Radius of circle A Diameter of circle B Answer: a) 3 units; b) 4 units; c) 2 units; d) 6 units Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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COPLANAR CIRCLES—Two circles can intersect in two points, one point, or two points. Coplanar circles that intersect in one point are called tangent circles. Coplanar circles that have a common center are called concentric. Image taken from: Geometry. McDougal Littell: Boston, P. 652.

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Common Tangents—A line, ray, or segment that is tangent to two coplanar circles is called a common tangent. Image taken from:

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**Ex.3: Tell how many common tangents the circles have and draw them.**

Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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**Ex.3: Tell how many common tangents the circles have and draw them.**

Answer: a. 2 common tangents; b. 4 common; c. 3 common tangents Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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Theorem 10.1and 10.2: In a plane, a line is tangent to a circle if and only if the line is perpendicular to a radius of the circle at its endpoint on the circle. Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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Ex.4: Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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Ex.4: Answer:No =4225, but 672=4489 Image taken from: Geometry. McDougal Littell: Boston, P. 653.

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Ex.5: Image taken from: Geometry. McDougal Littell: Boston, P. 654.

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Ex.5: Answer: 14 cm Image taken from: Geometry. McDougal Littell: Boston, P. 654.

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**Tangent Segments from a common external point are congruent.**

Theorem 10.3: Tangent Segments from a common external point are congruent. Image taken from:http://www.partnership.mmu.ac.uk/cme/Geometry/CircleGeom/Images/Tangent.jpg

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Ex.6: Image taken from: Geometry. McDougal Littell: Boston, P. 654.

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Ex.6: Answer: 5.5 Image taken from: Geometry. McDougal Littell: Boston, P. 654.

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10.1, p. 599, #6-29 all

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Section 10 – 1 Use Properties of Tangents. Vocabulary Circle – A set of all points that are equidistant from a given point called the center of the circle.

Section 10 – 1 Use Properties of Tangents. Vocabulary Circle – A set of all points that are equidistant from a given point called the center of the circle.

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